Continuity: The recording of Jack's diatribe on yuppies is very different from the "live" version we saw earlier.
Continuity: When Jack dials Lydia's number, it's ended with "11". A couple minutes later, Anna is looking into the same phone book and dials the number ended with "38" or "30"
Continuity: Jack and Anne have a violent quarrel, upon which he grabs her from behind to calm her down. In the next shot, Anne is in Jack's arms facing him.
Audio/visual unsynchronized: After the little quarrel with Anne, Jack gets a call. When he picks up the phone, it still keeps ringing for a short moment.
Revealing mistakes: After the double date dinner at the Chinese restaurant Anne unlocks the door to the apartment and puts her keys in her purse. The next scene she is hugging Jack and you can clearly see the keys still in her hand.